Answer:
[tex]y=\dfrac67x-\dfrac67[/tex]
Step-by-step explanation:
From inspection of the graph, we have been given two points on the line:
[tex]\textsf{let}\:(x_1,y_1)=(1,0)[/tex]
[tex]\textsf{let}\:(x_2,y_2)=(8,6)[/tex]
Therefore:
[tex]\textsf{slope}\:(m)=\dfrac{6-0}{8-1}=\dfrac67[/tex]
Point-slope form of linear equation: [tex]y-y_1=m(x-x_1)[/tex]
(where m is the slope and (x₁, y₁) is a point on the line)
Substituting the values of m and (x₁, y₁):
[tex]\implies y-0=\dfrac67(x-1)[/tex]
[tex]\implies y=\dfrac67x-\dfrac67[/tex]
Therefore, the equation of the line in slope-intercept form is:
[tex]y=\dfrac67x-\dfrac67[/tex]
